Let $g$ be a twice differentiable function, and let $g(7)=-5$, $g'(7)=0$, and $g''(7)=0$. What occurs in the graph of $g$ at the point $(7,-5)$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $(7,-5)$ is a minimum point. (Choice B) B $(7,-5)$ is a maximum point. (Choice C) C There's not enough information to tell.
Explanation: Since $g'(7)=0$, we know that $x=7$ is a critical point. The second derivative test allows us to analyze what happens in the graph of $g$ at this point according to these three cases: If $g''(7)>0$, the graph of $g$ has a minimum point at $x=7$. If $g''(7)<0$, the graph of $g$ has a maximum point at $x=7$. If $g''(7)=0$, the test is inconclusive. [Why is this so?] We are given that $g''(7)=0$. The test is inconclusive. There's not enough information to tell whether $(7,-5)$ is a minimum point, a maximum point, or neither.